ABSTRACT - Bulgarian Academy of Sciences3 INTRODUCTION Various methods have been proposed and used...

BULGARIAN ACADEMY OF SCIENCES

Institute of Information and Communication Technologies

RESEARCH ON NEURAL NETWORKS BASED CAPITAL

MARKETS FORECASTING MODELS

ABSTRACT

Thesis for awarding educational and scientific degree PhD

Scientific Field: 4. Natural sciences, mathematics and informatics

Professional Area: 4.6. Computer sciences

Scientific Specialty: 01.01.12 Informatics

Veselin Lazarov Shahpazov

Scientific Advisor: Acad. Ivan Popchev

Sofia

2019

2

Thesis Data:

• Number of Pages: 148

• Number of Figures: 21

• Number of Tables: 12

• Number of References: 139

• Number of Author’s publications on the subject of the Thesis: 6

3

INTRODUCTION

Various methods have been proposed and used to forecast the capital market over the

years based on technical analysis, fundamental analysis and statistical indicators with varying

degrees of success. However, no technique or combination of techniques has been successful

enough to "conquer the market" permanently, guessing its direction and the magnitude of its

movements.

With computing technology advancements and developments in the field of artificial

neural networks, researchers and investors are hoping to successfully acquire the ability to

untangle complex "market nodes" that will allow them to build a successful trading strategy.

This PhD Thesis will look at some traditional stock market and other financial instruments

traded on the capital market forecasting techniques, focusing on why they are not sufficient for

constant correct forecasting and how neural networks are used and could be used to improve

the forecasting process.

Among the many techniques in the field of Artificial Intelligence, the ones that best deal

with uncertainty are neural networks. Dealing with financial uncertainty involves a basic

recognition of trends in databases and the use of these trends to predict future events. Neural

networks handle issues such as insecurity and risk, better than other Artificial intelligence

techniques because they work well with large and imprecise databases. Unlike expert systems

and rule-based systems, neural networks are not so clear and the results obtained through their

use cannot be so easily explained, which makes them difficult to interpret.

Neural networks are used to predict stock market prices as they are able to learn

nonlinear relationships between the input of the system and its output. Contrary to the "Effective

Market Hypothesis" thesis, several researchers argue that the stock market and other financial

markets are chaotic systems. Chaos is a non-linear deterministic process that has the

characteristics of being random because it cannot be easily expressed. Using the ability of

neural networks to study chaotic, nonlinear systems, it may be possible to achieve better results

than traditional analysis and other computer-based forecasting methods. Because the use of

neural networks in the financial sphere is so extensive, this work will focus on using them to

predict stock market equity indices, especifically, the onese on the Bulgarian market.

The main tasks of the PhD Thesis as defined in its title, is to conduct a study on models

for forecasting the capital market with neural networks. Formulated are the following six tasks,

the solution of which will lead to achieving of this goal:

- Research of the formation, development and ability of neural networks to forecast the

capital market.

- Analysis of the methods for forecasting capital markets with neural networks.

- Researching the Bulgarian stock market as a subject of forecasting.

- Formulating a hybrid model for capital market forecasting.

- Carrying out experiments with the hybrid model in the real life conditions on the

Bulgarian capital market.

- Summary of the achieved results and future development of the model.

4

CHAPTER I: CAPITAL MARKETS FORECASTING MODELS

In this chapter, the traditional analytical methods used to forecast capital markets are

discussed: Fundamental Analysis, Technical Analysis, Dynamic Row Forecasting, Effective

Market Hypothesis, Chaos Theory, and Other Capital Market Forecasting Techniques.

Stock exchanges, as they are most commonly called, are official markets for financial

instruments, which are governed by rules. Another commonly used term is a Multilateral

Trading Facilities - organized by a market operator, through which the trading of financial

instruments is carried out in manner organized by the market operator and in accordance with

the national and/or international legislation. Until recently, official markets were the only

trading venues, but this has changed after the introduction of the Markets in Financial

Instruments Directive, known as MiFID. This directive decentralized this industry and allowed

the organization of Multilateral Trading Facilities, which significantly changed the marketplace

by improving liquidity, thus complicating access to such venues and causing the mass

introduction of algorithmic trading. There is only one such multilateral stock trading system in

Bulgaria, organized by the investment intermediary Capman AD called MTF Sofia.

Artificial neurons have been developed to model biological neurons in the human body.

The artificial neural network is made up of numerous artificial neurons that appear as

computational elements, connected together by weighted links and organized in layers. To

model the natural process in the human body with respect to the electrical activity of a neuron

like this: a neuron receives electrical signals from other neurons, collects all these signals to

calculate all the energy received, meanwhile part of that energy is lost, to overcome the natural

resistance level of the neuron and the rest of the energy is relayed to the next neurons from the

network

Perhaps the first work in the vast field of stock market price forecasting using artificial

neural networks, was the work of Hubert White in 1988, the author of which seeks to refute the

Effective Market Hypothesis. In its simplest form, the hypothesis states that asset price

movements are random, which means that price movements are absolutely impossible to guess

in advance, based on publicly available information such as market price and market volume

and historical prices. The purpose of the paper was to illustrate how the search for any patterns

that may indicate the future movement in the price of IBM common stock using artificial neural

networks and the change in stock price, can be successful. The topology of the network used is

the standard feed forward network with one hidden layer with full interconnectivity, with the

activation of the hidden layer transmitted to the output. The author uses a network with three

layers, five inputs and five neurons in the hidden layer. The choice of five hidden units is a

compromise in the need to include enough hidden units so that the simplest nonlinear

regularities can be found by the network. The training was done using the backpropagation

algorithm, one of the most popular to this day.

Research in this field has grown exponentially over time. The models are enriched by

artificial neural networks of various types and structures. Research objects vary, with the most

common and influential indices of traded stocks being the most common target Indices such as

the Dow Jones Industrial Average, S&P 500, Nasdaq, Euro Stoxx 50, FTSE 100, DAX 30,

Nikkei 225, CSI 300 and many others. The data used as inputs in most cases is price

information, data for traded volumes, technical indicators etc. In some situations, authors resort

to more non-standard data, such as analyzing minutes of central bank meetings and even

sentiment in specialized social networks.

In addition, Chapter One gives an overview of the stages in the development of neural

networks and the use of other techniques in artificial intelligence tools for forecasting financial

markets and capital markets in particular.

5

CAPTER II: ANALYSIS OF THE NEURAL NETWORKS BASED CAPITAL

MARKETS FORECASTING METHODS

The neurons in the neural networks are organized in layers. They can be of three types:

input, output and hidden. The input layer receives information from the external environment

only with each neuron corresponding to an input variable. No calculations are made in the input

layer, it transmits the information to the next layer. The output layer produces the final results

that are fed from the network out of the system. Each neuron in the output layer corresponds to

the values of the predicted variable. The layers located between the input and output layers are

called hidden because they do not come into direct contact with the external environment. The

hidden layers are used entirely for analytical purposes. Their function is to detect existing

relationships between input and output variables.

The architecture, also known as the topology of an artificial neural network, represents

its organization, namely: the number of layers, the number of elements (neurons) in each of the

layers, and the way the neurons are connected to each other.

Other intrinsic features are the direction of movement of the information (the direction

in which the calculations are made, and the type of relationships between the individual

elements.

A neural network with more than one layer of weighted neurons containing one or more

hidden layers is called a multilayer neural network, the most commonly used being the

multilayer perceptron.

Different information flows result in different types of neural networks. For feedforward

neural networks, information moves only in one direction, from the input layer through the

hidden layers to the output layer, and there are no return cycles. Feedback neural networks

move information in both directions, from the input layer to the output layer and vice versa.

If each element of one layer is connected to all elements of the next layer, the artificial

neural network is called completely interconnected; if each element is connected to each

element of each layer, the artificial neural network is called fully connected

In this chapter a detailed historical overview of the application of neural networks for

forecasting financial markets and stock prices. As can be seen from the graph below that in

20.75% (eleven of the articles) the authors found the performance of artificial neural networks

unsatisfactory or less successful than the methods by which they were compared, while in other

studies (79.25%) the conclusion is positive. Figure 1 shows schematically this observation.

Figure 1: Positive/Negative results from reviewed papers, according to their authors

79.25%

20.75%

Result of the reviewed scientific articles according to their authors

Изкуствените невронни мрежи се справят с поставената задача

Изкуствените невронни мрежи не се справят с поставената задача

6

Among the architectures used, the most prominent is the multilayer perceptron (MPL),

used 37 times. Among the less popular varieties are radial basis function neural networks

(RBFNN) used 3 times, probabilistic neural networks (PNN) used 4 times and general

regression neural networks (GRNN) only once. In the category of other architectures, where

the number is 19, it should be noted that there are some new or at least more popular, in more

recent studies structures, such as short and long memory networks and deep learning neural

network, along with considered more traditional recurrent neural networks (RANN). Figure 2

shows the distribution of neural network types in the studies considered.

Figure 2: Used neural network architecture

The forecasted types of markets are another reviewed criterion as developed markets

have been the subject 32 times followed by emerging markets with 14 forecasts. It is no

coincidence that the author's idea is to focus on the niche of unexplored and little-known

markets like the Bulgarian, presented by a study. Figure 3 shows the breakdown by type of

labor market.

Figure 3: Forecasted type of market

0 5 10 15 20 25 30 35 40

Изкуствени невронни мрежи с разпространение на информацията …

Изкуствени невронни мрежи с радиалнабазова функция (RBFNN)

Изкуствени невронни мрежи с обща регресия (GRNN)

Вероятностни изкуствени невронни мрежи (PNN)

Други

NN Architectures used

0

5

10

15

20

25

30

35

Развит пазар на акции

Развиващ се пазар на акции

Пазар на акции в централна, източна Европа и близкия

изток (CEEME)

Друг

Market classification subject to study

7

The scientific papers reviewed tend to be the subject of research into major global

markets in developed countries and stocks and indices of stocks of multinationals traded in

some cases in several different markets, as well as broader industry indices .

Although low liquid and underdeveloped markets, also known as frontier markets

present an environment of low liquidity and the dependence on events on the global economic

scene is much less pronounced, there is an opportunity to test the ability of artificial neural

networks to predict such markets as well.

8

CHAPTER III: RESULTS FROM RESEARCH ON NEURAL NETWORKS BASED

CAPITAL MARKETS FORECASTING MODELS AND PROPOSED NEURAL

NETWORKS AND RULE-BASED SYSTEMS HYBRID MODEL FOR FORECASTING

THE CAPITAL MARKET

This chapter begins with a brief history of the Bulgarian stock market, describing its

structure and classifying it as an illiquid and undeveloped stock market.

The data used for the experiments conducted in this chapter are from the official site of

the Bulgarian Stock Exchange and consist of the following information about the SOFIX index:

latest value, opening value, highest value of the day, and lowest value of the day, as well as the

volume traded. In addition to the price information, five of the most common technical

indicators are used in the experiment: 30-day moving average, 60-day moving average, 200-

day moving average, 14-day relative strength index and 30-day relative strength index. All data

are for the period between 04/01/2010 and 02/28/2013.

After the initial selection of the data, the selected data is divided into three parts, half of

which is used for actual training and the rest is divided between test data and validation data or:

training data - 50%, test data - 25% and validation data - 25%.

Three different networks are tested starting with most widely used multi-layer

perceptron, a feed-forward artificial neural network model that maps sets of input data onto a

set of appropriate outputs. A multi-layer perceptron consists of multiple layers of nodes in a

directed graph, with each layer fully connected to the next one the network utilizes a supervised

learning technique called back-propagation for training the network it is the most popular

algorithm and is extremely simple to program but tends to converge slowly. It calculates the

local gradient of each weight with respect to each case during training. Weights are updated

once per training case.

The formula is:

)1()( −+= tt ijijij (1)

Where:

η – the learning rate;

δ - the local error gradient;

α - the momentum coefficient;

𝑜𝑖 – the output of the i'th unit.

Thresholds are treated as weights with 𝑜𝑖 = -1. The local error gradient calculation

depends on whether the unit into which the weights feed is in the output layer or the hidden

layers. Local gradients in output layers are the product of the derivatives of the network's error

function and the units' activation functions. Local gradients in hidden layers are the weighted

sum of the unit's outgoing weights and the local gradients of the units to which these weights

connect.

The Conjugate gradient descent is an advanced method of training multilayer

perceptron’s. It usually performs significantly better than back propagation, and can be used

wherever back propagation can be. It is the recommended technique for any network with a

large number of weights (more than a few hundred) and/or multiple output units. Conjugate

gradient descent is a batch update algorithm: whereas back propagation adjusts the network

weights after each case, conjugate gradient descent works out the average gradient of the error

surface across all cases before updating the weights once at the end of the epoch.

9

In the process of back propagation, the gradient vector of the error surface is calculated.

This vector points in the direction of the steepest descent from the current point, so if we move

in this direction even for a short distance, we will reduce the error. The sequence of such

movements will eventually find some minimum. The difficult part is deciding how big the steps

should be. Big steps can get you closer to the minimum value of the error faster, but they can

also skip it, or (if the surface of the error is very eccentric) go in the wrong direction. Usually,

the algorithm is modified by including an inertia moment in the training. This encourages

movement in a certain direction, so that if several steps are taken in the same direction, the

algorithm increases its speed, which sometimes enables it to escape from local minima as well

as to move quickly over flat spots and fabrics. The initial network configuration is random, and

training stops when a number of epochs expire, when the error reaches an acceptable level, or

when the error stops improving.

One major problem with this type of training is that it does not actually reduce the error

that is really of interest - such as the expected mistake the network will make when new cases

other than the one it is trained on are presented. In other words, the most desirable ability of a

network is its ability to generalize or generalize to new situations.

The most important manifestation of this distinction is the problem of overfitting. An

artificial neural network with more weights models a more complex function and is therefore

prone to over-training. A smaller weight network may not be powerful enough to model the

underlying function. For example, a network without hidden layers actually models a simple

linear function. When learning the network excessively during the training process, it is usually

recommended to reduce the number of hidden units and / or hidden layers as the network is too

powerful for the specific problem. In contrast, if the network is not powerful enough to model

(has less than the required optimal number of units and hidden layers) the core function will not

result in over-training, but neither training errors nor error test will fall to a satisfactory level.

The final model is tested with validation data to ensure that its learning and testing

results are real. Of course, to fulfill this role successfully, the validation set must be used only

once. If it, in turn, is used to adjust the network parameters and repeat the learning process, then

the process becomes a data selection.

The process of data separation is highly subjective, and in theory there are various

different theories as to how it should be conducted. This problem can be overcome by

reclassifying individual databases. Experiments can be performed using different selections of

available data in training, testing and validation groups. There are a number of approaches to

this transformation of subsets, including random calculations (Monte Carlo), cross validation,

and bootstrap. Another approach is to retain only the best networks found during the test and

validation process, based on different samples, but to average their results, which will reduce

the subjective factor in the allocation of data sets.

The most widely used activation function for the output layer are the sigmoid and

hyperbolic functions. In this paper, the sigmoid transfer function is employed and is given by

(2)

The error of a particular network configuration can be determined when all network

training cycles are completed by comparing the actual generated predicted value with the

desired or target results. The differences are combined by an error function to calculate the

network error. The most common error measure (used for regression problems) is the root mean

10

square error where the individual errors of the output units are in each case squared and summed

together.

The criteria which will evaluate the Neural Networks performance will be the error of

the network on the subsets used during training (Root Mean Square-RMS).

(3)

As many authors have recommended that in order not to slow down the constructed

model and to delay its calculation time further, the data submitted to be of smaller order was

considered as having to reorganize the data from values in daily change of the original ones.

values. This is determined by the number of input variables, which are ten over a period of two

years and two months.

Initial study results are not particularly good. They show an interesting trend, namely

that networks that use all ten input parameters are constantly performing much worse than those

that isolate some of the input parameters. Models that base their forecasts solely on the last

price show the best results in terms of learning error. Moreover, in no case did a network with

more than one hidden layer perform better than one with a single hidden layer.

Several types of architecture were tested, with the best performing artificial neural

network having three layers, with one element in the input layer responsible for the last-change

parameter, which was the ultimate goal of forecasting and using 43 lagged steps. This model

has 7 elements in the hidden layer, and one element in the output layer corresponding to the

predicted input variable. The structure was selected using the model structure optimization

feature available in the software product provided, which proved to be more efficient and much

faster than manual adjustments made by the author. Training on the best performing network at

this stage involves 100 cycles (epochs) of back propagation and 23 cycles of conjugate gradient

descent. This led to a test error of 0.119279, which at first glance may lead to two conclusions.

The first is that the network has not been over-trained and the second is that the result certainly

does not look impressive.

After taking into account the achieved initial results, it is evident that some adjustments

should be made to the model, which is why the author turned to the input data. Taking into

account the peculiarities of the Bulgarian stock market, and in particular its illiquidity, which

allows individual transactions not executed on a purely market principle to affect the overall

value and an index change, it was considered appropriate to undertake additional preliminary

data processing in the form of averaging of the input values, respectively, of the index changes

starting from 3 days averaging. The results of such experiments are presented in the following

table:

11

Network structure

Input-hidden-output

Learning samples

BP/CGD

Test error

RMS

3 days smoothing 1(12)-5-1 BP-100; CGD-115 0.076298







Table 1: Results from smoothing input data

It is evident from the results in the table that the averaging performed results and

manages to reduce the error in the validating data set significantly. There is a tendency for the

error to continue to decrease as the averaging period is extended to 7 days. Then the error starts

to grow again and loses, and the continuation of the averaging loses its meaning. The neural

network that performed best in the form of the smallest validation error value of 0.057099 was

built from a single input layer (and here again the tendency to better represent networks using

only the predicted parameter as input), 13 neurons in the hidden layer and one output element.

The training was performed on the basis of 34 epochs of conjugated gradient descent and 100

epochs of back propagation and data 20 steps back in time. It can be seen from the table that

the epochs of learning by back propagation are limited to 100, due to the time consuming nature

of this type of training and the lack of better results when conducting experiments without

setting a maximum number of cycles. A figurative representation of the best performing neural

network is shown in Figure 4

Figure 4: Multilayer perceptron with 10 inputs, 13 hidden neurons and one output

Figure 5 shows the predicted results from actual observations of a multilayer perceptron

with 10 inputs, 13 neurons in the hidden layer, and one output element

12

Figure 5 shows the predicted results from actual observations of a multilayer perceptron

with 10 inputs, 13 neurons in the hidden layer, and one output element

Figure 5: Predicted values versus observed plot

Predicted change (dotted line) versus observed changeis presented on Figure 6.

Figure 6: Predicted change (dotted line) versus observed change

Residual error diagram respectively of the multilayer perceptron with 10 inputs, 13

hidden neurons and one output presented on Figure 7.

13

Figure 7: The residual error diagram

An interesting trend can be seen from the residual error graph shown in Figure 7. An

increase in the magnitude of the error is observed at the beginning of the period and its end,

which can be explained by the composition of the input data presented on the artificial neural

network. In the first part of the observed period, the Bulgarian stock market is in an upward

trend, with the index rising by more than 23% in about a month. At the end of the observed

period, the index first rose with an increase of more than 26% for about a month and a half, and

then there was a strong correction (a sharp withdrawal from the achieved high values) in its

value of 11% within a few days, which According to the author, the chart also leads to a jump

in the deviation of the network's predictions from the actual values of Sofix.

Another observation of the averaged data experiment is the continued poor performance

of neural networks using the full set of 10 parameters for training, testing and validation. The

best result was obtained from a model using 9 of the variables, with averages over 7 days. The

network was made up of 9 input elements responsible for the nine variables used, 21 neurons

in the hidden layer and one element in the output layer, trained based on 100 cycles of error

back propagation and 81 cycles of conjugated gradient descent. The result for the root mean

square error is 0.068935 and is still considered not good enough, especially considering the

more complex structure of the neural network and most of the time it takes to train it.

An experiment on two BSE Sofia indexes with different network architectures is

presented below.

Radial basis function networks have a number of advantages over MLPs. First, as

previously stated, they can model any nonlinear function using a single hidden layer, which

removes some design-decisions about numbers of layers. Second, the simple linear

transformation in the output layer can be optimized fully using traditional linear modeling

techniques, which are fast and do not suffer from problems such as local minima which plague

multilayer perceptrons training techniques. Radial basis functions networks can therefore be

trained extremely quickly. Figure 8 illustrates the way in which neural networks with radial

basis function are represented schematically.

14

Figure 8: Radial basis function network

Unlike radial basis networks, multilayer perceptron becomes more secure in long-range

results. Whether this can be considered an advantage or a disadvantage depends largely on the

application, but in general, extrapolation of the multilayer perceptron is considered a weak point

(extrapolation away from training data is usually considered dangerous and unjustified).

Networks with a radial basis function are also more sensitive to the scale of the input

and have greater difficulty if the number of input units is large. One aspect of the so-called

"curse of dimension" is that as the number of predictors increases (due to the increase in the

number of inputs), the variance also increases. The higher the value of the variance, the more

difficult it is for the predictive algorithm to perform well when the network is fed with new

data.

The ratio of the input to the output layer of an artificial neural network with a radial

basis function is defined as follows:

(4)

where 𝜇𝑗(𝑛) is the center point of the j-th Gaussian unit, the width σ(n) is common to all

the K units, and 𝑤𝑗(𝑛) is the linear weight assigned to the output of the j-th unit; all these

parameters are measured at time n- the cost function used to train the network is defined by

(5)

where:

This is a convex function of the linear weights in the output layer, but not convex with

respect to the centers and widths of the Gaussian units.

Radial basis function neural networks can also be hybridized in several ways. The radial

layer (hidden layer) can be trained using the Kohonen and Learned Vector Quantization training

algorithms, which are alternative methods of identifying centers to reflect data distribution, and

the source layer (linear or not) can be trained , using any of the iterative point algorithms

available to the author.

15

The third network type used for the forecasting procedure is the general regression

neural network. The general regression neural network performs regression where the target

variable is continuous as opposed to the probabilistic neural networks (they both have similar

architectures), which performs classification where the target variable is categorical. Proposed

by D. Spach, they are a one-way training algorithm for passing training information through it,

with a highly parallel structure. These types of neural networks are capable of providing a

smooth transition from one observation to another even with incomplete data in a

multidimensional measurement space. The algorithmic form can be used for any regression

problem in which the assumption of linearity is not justified.

The mathematical representation and schematic form of the general regression networks

are shown in Figure 9 below

(6)

(7)

where: m is the number of clusters

А𝑖(k) и 𝐵𝑖(k) – are the values of the clusters coefficients i after k observations

А𝑖(k) is the sum of Y values

𝐵𝑖(k) is the number of patterns for cluster i

𝜎 is the width probability

(8)

16

Figure 9: General regression neural network

A general regression neural network performs a regression in which the target variable

is continuous, which performs a classification in which the target variable is categorical. The

main advantages over multilayer perceptrons are:

- It is usually much faster to train a general regression neural network than a multilayer

perceptron network.

- Probabilistic neural network/General regression neural networks often are more

accurate than multilayer perceptron networks.

- Probabilistic neural network/General regression neural networks are relatively

insensitive to outliers (wild points).

- Probabilistic neural network/General regression neural networks generate accurate

predicted target probability scores.

The respective shortfalls of General regression neural networks are:

- Probabilistic neural network/General regression neural networks are slower than

multilayer perceptron networks at classifying new cases.

- Probabilistic neural network/General regression neural networks require more memory

space to store the model.

17

The only control factor to choose when training networks with general regression is the

smoothing factor (ie, the radial deviation of the Gaussian functions). As with networks with

radial basis functions, this factor must be chosen to cause reasonable overlap - too small

deviations cause a very tangible approximation, which cannot generalize while too large

deviations smooth out the details. The appropriate digit can easily be selected by experiment

by selecting a number that results in a low selection error, and fortunately, networks with

general regression are not too sensitive to the exact selection of the smoothing factor.

Apart from Sofix, the other index to be considered in this section is BG40. It is based

on emission pricing and covers 40 issues of ordinary shares of the companies with the highest

number of transactions and the highest average daily turnover over the last 6 months, with both

criteria being equally weighted.

The object of the experiment will again be the prediction of the values of the two indices

in the future, based on previous information.

The data for the experiment are from the official site of BSE - Sofia AD, composed of

price information on a daily basis for the two indices from 04.01.2010 to 28.02.2013 and more

precisely: closing value, opening value, max. higher value for the day and lowest value for the

day. On the basis of previous studies conducted by numerous researchers, as well as the

experience of the previous experiment, it was decided to differently distribute the data in the

three subsets, namely training, testing and validation. This was done with 70% of the data set

for training, 15% for testing and 15% for validation. This is mainly due to the results of the

multilayer perceptron in predicting the Sofix index from earlier and the author's desire to do

less pre-processing of the data.

At the beginning of this experiment, it was decided not to perform any refinement of the

initially generated databases for Sofix and BG40, due to the fact that the first results of the three

types of networks showed no improvement after converting the digital values of the indices into

daily changes. Selected criteria for evaluating network performance is again the network error

of subsets used during training - the mean square error. In mathematics, the term is explained

as a statistical measure of the magnitude of a variable.

The multilayer perceptron was again trained with back propagation and conjugate

gradient descent algorithms, while the other two network architectures did the same. Radial

basis function networks were trained based on the k-means (K-Means), k-nearest-neighbor (K-

Nearest Neighbor) and pseudo-inverse algorithms. Artificial neural networks with general

regression were trained with Subsampling algorithm.

The results of the forecasting of the SOFIX index are presented in Table 2 below.

18

Neural network

name Training algorithm Inputs

Hidden

(1)

Hidden

(2) Test Error

1

Multilayer

perceptron 1

Back-propagation,

Conjugate gradient descent 1 3 0 0.023607

2

Multilayer

perceptron 2

Back-propagation,


3

Radial Basis

Function NN 1

K-Means, K-Nearest

Neighbor, Pseudo-inverse 1 42 0 0.001892

4

Radial Basis

Function NN 2

K-Means, K-Nearest


5

General

regression

neural network 1

Subsampling algorithm

1 533 2 0.000832

6

General

regression

neural network 2


2 533 2 0.000741

Table 2: Forecasting Sofix Index

As can be seen in the test results table, the best result, expressed as the smallest

validation error (Test Error), was achieved by neural networks with a common regression. The

most successful network consists of 2 elements in the input layer, 553 elements in the first

hidden layer, 2 elements in the second hidden layer, and one element in the output layer

corresponding to the requested variable. The error generated by the better performing network

was 0.000741 and for the second one 0.000832, both of which were trained on the basis of the

Subsampling algorithm.

Artificial neural networks with radial basis function show constant and good results,

with the two best performing models showing error of 0.001892 and 0.002034 respectively.

Structured of 1 and 4 elements in the input layer, both have 42 elements in the hidden layer and

one output element corresponding to the desired variable, both of which are trained using the

k-means (K-Means) algorithms, k - closest neighbor (K-Nearest Neighbor) and pseudo-inverse.

The K-Means algorithm attempts to select the optimal set of points that are located in the centers

of training data groups. For given K radial units, it adjusts the positions of the centers so that

each training point belongs to the cluster center and is closer to that center than to any other

center, and each cluster center is the center of the training points that belong. Once the centers

are set, the deviations are set. The magnitude of the deviation, also known as the smoothing

factor, determines how prominent the Gaussian functions are. For K-Nearest Neighbor, each

unit deviation is individually set at a mean distance to K-Nearest Neighbor. Therefore, the

deviations are smaller in tightly filled spaces, retaining details and higher in sparsely filled

spaces (interpolating where necessary). After the centers and deviations are set, the output layer

is optimized using the standard linear optimization technique - the pseudo-inverse (singular

value decomposition) algorithm.

Multilayer perceptron-type networks are the worst of the three models. The results of

their two best representatives are 0.023607 and 0.024466, respectively, produced by networks

19

made up of three layers having 1 input, 3 elements in the hidden layer for the first and 5 elements

in the hidden layer for the second, and one element in the output layer , corresponding to the

requested variable for both models. Trained with 100 epochs and 34 epochs of conjugated

gradient descent for the first and 100 epochs of reverse propagation and 34 epochs of conjugated

gradient descent for the second, they perform significantly worse.

Graphically, the forecasts of the six networks listed in Table 2 for the selected period

are shown in Figure 10

Figure 10: The values of the index and the predicted values by the three different

models (two of each) for the last 50 days of the observed period.

At this stage, some surprising facts cannot be ignored. First is the good results that show

both neural networks with general regression and those with radial basis function. They seem

to do much better in modeling the input data, managing to produce equally good results by

isolating a different number of input parameters. For example, the second best network with

general regression uses two neurons in its input layer, respectively, responsible for the target

variable - the last index value of the day (close value) and the lowest value for the day, while

the second best network with radial base function uses all 4 input parameters (except the above

two and the opening value and lowest value for the day).

Although the results of the multilayer perceptron were better than those achieved during

the first experiment, they remained many times worse than those of the models described above.

This trend is visible not only in validating data, but also on the basis of error data during training

and network testing. Table 3 presents the error data of the six models during training and in the

test data set.

360

370

380

390

400

410

420

756 761 766 771 776 781 786 791 796 801

Ind

ex

Val

ue

SOFIX: прогнози съпоставени с действителни наблюдения

SOFIX

MLP1

MLP2

RBF1

RBF2

GRNN1

GRNN2

20

Neural network

name Training algorithm

Train

Error Select Error

1

Multilayer perceptron

1

back-propagation,

conjugate gradient descent 0.020964 0.023328

2

Multilayer perceptron

2

back-propagation,

conjugate gradient descent 0.020729 0.023204

3

Radial Basis Function

NN 1

K-Means, K-Nearest

Neighbor, Pseudo-inverse 0.001732 0.002120

4

Radial Basis Function

NN 2

K-Means, K-Nearest

Neighbor, Pseudo-inverse 0.001937 0.002068

5

General regression

neural network 1 Subsampling algorithm 0.000962 0.000877

6

General regression

neural network 2 Subsampling algorithm 0.000785 0.000697

Table 3: Neural network’s error during training and testing on Sofix Index data

When predicting the BG40 index, the situation was not much different. Artificial neural

networks with general regression were again the most productive and reached the lowest values

in the validation set. The lowest error value was 0.004963 achieved by a network consisting of

2 elements in the input layer, 550 elements in the first hidden layer, 2 elements in the second

hidden layer, and one element in the output layer corresponding to the predicted variable. This

time the input parameters used are the last index value of the day and its highest value for the

day. Unlike before, the second best network of this type uses one element in the input layer,

550 elements in the first hidden layer, 2 elements in the second hidden layer, and one element

in the output layer corresponding to the predicted variable. The achieved results for its error

value is 0.005467. Both networks are trained on the basis of Subsampling algorithm.

The second result is a network architecture with a radial basis function with 2 elements

in the input layer, corresponding to the parameters last index of the day and highest index of

the day, 30 elements in the hidden layer and one element in the output. This structure also has

the second best network of its kind, but it uses all 4 parameters to make its forecasts. The results

obtained with respect to the error value are respectively 0.014879 for the first and 0.0155 for

the second. Both networks are trained using the k-means (K-Means), k-nearest-neighbor (K-

Nearest Neighbor) and pseudo-inverse algorithms.

Again, third place is occupied by multilayer perceptrons, which manage to shorten the

distance between their presentation and that of the next model, by utilizing one element in the

input layer, one for the better mesh and two elements in the hidden layer of the second network,

respectively. one element in the output layer. The results obtained with respect to the error value

are respectively 0.032738 for the first and 0.032934 for the second. In this case too, training

based on 100 epochs and 28 epochs of conjugate gradient descent for the first and 100 epochs

of dissemination and 18 epochs for conjugated gradient descent for the second is not good

enough for these models to compete with the others.

A table summarizing the results of the three network architectures used to predict BG40

is shown in Table 4.

21

Neural

network name Training algorithm Inputs

Hidden

(1) Hidden(2)

Test

Error

1

Multilayer

perceptron 1

Back-propagation,


2

Multilayer

perceptron 2

Back-propagation,


3

Radial Basis

Function NN 1

K-Means, K-Nearest


4

Radial Basis

Function NN 2

K-Means, K-Nearest


5

General

regression

neural network

1


1 550 2 0.005467

6

General

regression

neural network

2


2 550 2 0.004963

Table 4: Forecasting BG40 Index

Figure 11: The values of the index and the predicted values by the three different

models (two of each) for the last 50 days of the observed period.

The BG40 forecasting task again confirms the good results shown by neural networks

with general regression. Generally, the errors in all three varieties increase over those produced

by Sofix's forecasting, which is probably due to the higher volatility of the index and some other

factors related to the selection of input data.

122

124

126

128

130

132

134

136

138

751 756 761 766 771 776 781 786 791 796

Ind

ex

Val

ue

BG40: Forecasts compared to actual observations

BG40

MLP1

MLP2

RBF1

RBF2

GRNN1

GRNN2

22

Based on the study of the possibility of forecasting the indices on the Bulgarian stock

market with three of the numerous types of artificial neural networks, it can be concluded that

this class of models in the field of artificial intelligence can successfully cope with the task of

predicting future values related to with financial instruments based on time series financial

information. It should be made clear at once that this does not in any way mean that they are

capable of trading successfully on the financial markets, furthermore that the experiments

carried out do not imply such an opportunity. On the other hand, they are certainly capable of

supporting a more complex model aimed at real trading on the stock market, even in conditions

such as those on the Bulgarian market.

Introducing a hybrid model built on neural networks and rule-based systems for trading

on BSE - Sofia.

Capital markets in different parts of the world are very distinct due to the difference in

many of its features. This work has already described in detail how big the differences between

developed and underdeveloped markets are. This inevitably leads to equally large differences

in the techniques applied in these markets, in order to gain an advantage over the other players

and, of course, to make a profit.

Sofia is Sofix. It is based on the market capitalization of the ordinary shares included in

it adjusted for the free float of each of them. The index covers 15 stocks that meet the general

emission selection requirements as well as additional quantitative requirements. The issues

included in Index calculation need to meet certain metrics including: a minimum trading period

before inclusion, a minimum market value of their free float, a minimum number of

shareholders holding the issue and a spread between buy and sell orders. Sofix is rebalanced

twice a year, with trading and other information being taken after the end of the trading sessions

on March 1st and September 1st, respectively. The final composition of the index is determined

after all the qualifying emissions are ranked according to 4 quantitative indicators with all four

weighted equally:

- biggest market value of their free float

- highest number of deals over the past six months

- highest median weekly turnover value over the past six months;

- the lowest average spread between buy and sell orders.

As of September 2016, the first exchange traded fund based on the Sofix Index started

trading on the BSE-Sofia floor (Expat Bulgaria SOFIX UCITS ETF). As of April 2019 the

fund’s total assets are slightly below BGN 25 million. The fund aims full physical replication

of the Index and is listed on the London and Frankfurt stock exchanges. The purpose of the

fund is to follow the performance of the index, with a minimum tracking error.

The Index is also used as a performance benchmark for the few foreign investment funds

that invested in the local market as well as lots of professionally managed individual portfolios.

All this makes the Index composition and rebalance extremely important. Which companies

remain in its composition and which companies leave it and which are added to its calculation

is of great importance for all market players. According to a observation conducted by the

authors on the basis of the stock price change for the last 5 rebalances of Sofix, the average

price change of the companies that fall out of its calculation is -8.35% for the period of one

month preceding the final due date for determining its composition, and the average change in

the prices of the companies added to its calculation is + 12.00% for the period of one month

before the final date for determining its composition.

The author of this paper proposes a hybrid model based on artificial intelligence

techniques: rule-based systems and neural networks, which predicts the composition of the

Sofix index before this being made by other market players

23

The information required to feed the model is publicly available and is generated by the

daily bulletin published by BSE – Sofia (Figure 1), containing all information on the daily

trading of all issues listed on it as well as the free float and number of shareholders newsletter

of each traded issue published by the Central Depository (Figure 2). The rules for determining

and calculation of the composition of the index will be taken from the rules for calculating the

indices of BSE-Sofia.

Rule-based systems use human experience-based knowledge to solve a variety of

problems that typically require human intelligence to solve. This knowledge is shaped as rules

or data in computer systems and programs. Depending on the problem being solved, the system

can use this knowledge. For this purpose they are composed of the so-called. a decision-maker

that evaluates which available knowledge to select and apply, as well as the knowledge modules

and rules attached to it. This element produces action instructions, classifications, etc., and one

of its advantages is that they are transparent and can be justified by the programmed rules and

patterns in the model or combinations thereof. In this respect, rule-based systems are different

from neural networks, which are often referred to as black boxes, the results of which are very

difficult to explain.

Based on the numerous considered works in the field of neural network financial time

series forecasting, it is proposed to use several network architectures, similar to the experiment

described in the preceding points, to ensure the selection of a better model for this vital part of

experiment. The network architectures chosen are those of the multilayer perceptron, neural

networks with radial basis function, and neural networks with general regression with which

the author has extensive experience. The neural network models will be used to predict the

future development of the main 4 indicators on the basis of which the emission classification

for the composition of Sofix is made. The idea is to make 2 types of forecasts: First one day

ahead based on the initially available information for the entire remaining period and second,

to generate dynamic data and include the results for each day forward produced by the networks

in the training data .

A schematic representation of the proposed hybrid model built from neural networks

and rule-based systems can be seen in Figure 12.

24

Figure 12: Rule-based system and neural network-based hybrid model

Supplemented database for the whole period

(real + estimated)

Rule-based system

Estimated shares ranking on the basis of all

criteria and Estimated composition of the

Sofix Index

Option 1: Buy

new issues to be

added to the

Index

Option 2: Sell

issues droping

out of the Index

Neural networks used to forecasting data for

the remainder of the period (till March 1 or

September 1, respectively)

Quantitative

criteria data for

BSE issues

Data Base 1: BSE - Sofia Bulletin

(trading data)

Data Base 2: Issuers free float and

number shareholders data from

Central Depository

Rule-based system

General criteria

for determining

the composition

of the Sofix Index

Preliminary result: Ranking of issues as of a

specific date (1 month before 1 March or 1

September)

25

As can be seen in Figure 12, the proposed model shows, the module with rules-based

systems is fed with information from the daily bulletins of Bulgarian Stock Exchange and the

Central Depository, for a period of five months, This comprises knowledge base of the module.

The rule module at this stage is made up of the general criteria for determining the Sofix index.

The result produced, in the form of a list of qualifying shares is submitted to the neural networks

module, which in turn performs forecasting of each of the four quantitative criteria on the basis

of a database of these criteria for each individual share on the list. After the neural networks

perform the forecasting, the resulting new database (built up of real and forecasted values) is

fed to a rule-based system for compiling new company rankings. It determines the final forecast

composition

26

CHAPTER IV: FUTURE WORK

Guidelines for future research can be drawn along two interconnected lines. The first,

with regard to refinement of neural network based capital market forecasting models, through

experiments with other types of networks, architectures, training techniques and various pre-

processing of the information provided in the models in order to improve their forecasting

capabilities. In this respect, the author sees potential in exploring the possibilities offered by

relatively new techniques in the field of machine learning, such as support vector machines

(SVMs) used for regression and classification. The second guideline is to further develop the

proposed hybrid model of neural networks and systems based on rules for forecasting

underdeveloped and low liquid capital markets aimed at complementing it by including an

additional element to deal with the highly subjective quantitative element for evaluating the

liquidity of the shares, namely the test of the spread between the buy and sell prices of fixed

amounts, which is calculated after discretionary observations at the exchange operator's

discretion during the exchange session. The author finds the technique in the field of Artificial

Intelligence - fuzzy decision-making systems suitable for this purpose.

It could also work towards testing and applying these models on other capital markets,

with similar performance in the Bulgarian capital, although this is related to many other

conditions, such as specific trading conditions in similar markets, different rules for defining,

maintaining and rebalancing indexes and more.

27

CHAPTER V: CONCLUSION - SUMMARY OF THE PRODUCED RESULTS WITH

THE DECLARATION OF ORIGINALITY OF THE THESIS WORK

In conclusion, the following findings can be made on the basis of the experiments

performed and the proposed hybrid model. In the first experiment with multilayer perceptron,

averaging the submitted data in an illiquid market conditions results and manages to reduce the

error in the validating data set significantly. There is a tendency for the error to continue to

decrease as the averaging period is extended to 7 days. Then the error starts to increase again

and the continuation of the averaging loses its meaning. Epochs of error propagation training

are limited to 100, due to the time consuming nature of this type of training and the lack of

better results when conducting experiments without setting a maximum number of cycles.

In particular, neural networks and multilayer perceptron perform well when forecasting

on a time series basis for consolidation-phase market information and lose precision in trend

conditions, especially in a downward trend.

Another observation from the averaged data experiment is the continued poorer

performance of neural networks using the full set of 10 parameters for training, testing and

validation.

The second experiment, conducted with three types of neural networks, produced some

surprising results. First, the good performance shown by both neural networks with general

regression and those with radial basis function. They seem to do much better in modeling the

input data, managing to produce equally good results by isolating a different number of input

parameters. For example, the second best network with general regression uses two neurons in

its input layer, respectively, responsible for the target variable - the last index value of the day

(close value) and the lowest value for the day, while the second best network with radial base

function uses all 4 input parameters (except the above two and the opening value and lowest

value for the day). Although the results of the multilayer perceptron were better than those

achieved during the first experiment, they remained several times worse than those of the other

models. This trend is visible not only in validating data, but also on the basis of error data during

training and network testing.

During the second part of the second forecasting experiment (the prediction of the more

volatile index), the good results again showing the neural networks with general regression

were confirmed. Generally, the errors in all three varieties increase over those produced in the

estimation of Sofix, which is probably due to the higher volatility of the BG40 index and some

other factors related to the selection of input data. There were no major shifts in the ranking of

the models compared to the previous experiment. To some extent, the use of 2 input parameters

from the most successful model, which happens for the first time, can be considered

unexpected, but in the previous case, the difference between the one that only relies on the

requested variable and the second most successful was too small.

The results of multilayer perceptron are worse than those achieved during the Sofix test,

but this, as mentioned above, is a general trend. They observe a convergence with the results of

networks with a radial basis function, which can be considered as a positive factor. The results

of the three models in terms of error during training and that of the test data retain the trends

imposed by the baseline assessment.

In summary, it can be stated that the results of the study of the prediction capabilities of

the three types of neural networks can be considered useful. Consistency in the results of neural

networks with general regression makes them unprecedented winners in this kind of

competition. Thus, they largely confirm their positive attestations, noted a priori by the

experiments performed, as being faster and more successful, able to handle data containing

deviations.

28

Very good and consistent performance is also reported for the model using a radial basis

function. They show success in handling more than one input parameter to predict the target

variable, which sets them apart.

The multilayer perceptron can be defined as the worst performing network in the

prediction of both indexes, and its poor results are confirmed both by the amount of error during

the validation data and by its training and testing. Although the size of the error it produces is

not large and if we abstract from the results of other models, its estimates can be considered

satisfactory and reliable, looking at things on a relative basis it is difficult to be complacent. It

is also a fact that for the more volatile BG40 index data, the difference from other models, and

in particular from those with a radial basis function, is greatly diminished.

Based on the study of the possibility of forecasting the indices on the Bulgarian stock

market with three of the many types of artificial neural networks, it can be concluded that this

class of models in the field of Artificial Intelligence can successfully cope with the task of

predicting future values related to with financial instruments traded on the Bulgarian capital

market based on time series financial information. It should be made clear at once that this does

not in any way mean that they are capable of successfully trading on the capital markets as a

standalone strategy for generating sales alerts, furthermore that the experiments conducted do

not imply such an opportunity. On the other hand, they are certainly capable of supporting a

more complex model aimed at real trading on the stock market, even in conditions such as those

on the Bulgarian market.

As a logical continuation of the conclusion from the first two experiments comes the

author's proposed hybrid model of neural networks and rule-based systems for trading on the

BSE - Sofia. The model is considered to be operational and applicable in the context of a low

liquidity and underdeveloped capital market. It is promising and has huge potential to be used

both to experiment with historical data for academic purposes, such as validating or rejecting

the theory of an effective market, and to support a real trading strategy in line with the low

liquidity, the absence of rich trading instruments (the practical impossibility of short selling,

margin purchases and the lack of derivative instruments) and the lack of many quality issuers

that can be characterized by and the Bulgarian stock market.

As a result of the research presented in this dissertation, certain scientific and applied

results have been achieved:

The possibilities for forecasting capital markets with neural networks have been

investigated. The formation, development and ability of neural networks to forecast the capital

market was investigated. Particular attention has been paid to the evolution and development

of this endeavor globally over the years, as well as to the various approaches that have been

offered and used.

A study was conducted on the state of play in the forecasting of the neural network

capital markets, with a review of a large number of books, articles and publications on the topic,

of which more than 50 papers were reviewed and analyzed, from which interesting conclusions

were drawn for preferred from the authors models, architectures and methods of training neural

networks. Also, a summary of the capital markets, stock indices and types of inputs predicted

and used by the models is made, as well as an examination of the use of other techniques in the

Artificial Intelligence field for capital market forecasting.

As part of the study on the Bulgarian stock market, which is the subject of forecasting,

a presentation was made on the Bulgarian regulated capital market in the face of BSE - Sofia

and the main qualitative and quantitative differences between it and the developed exchanges

around the world were determined, on the basis of which defines as not well developed.

A hybrid model of neural networks and systems based on rules for forecasting a

undeveloped and low liquid capital market such as that in Bulgaria is proposed. The author

finds this model workable and extremely promising, with enormous potential to put into use

29

both those who wish to experiment on past historical data for academic purposes, such as

exposing the “Effective Market Hypothesis” and supporting a real-world one. trading strategy

tailored to low liquidity conditions, lack of rich trading tools.

The experiments carried out with the created hybrid model in the real conditions on the

Bulgarian capital market, on the basis of data from past periods, confirm its capabilities.

The summarized results of the experiments performed and the results obtained can be

summarized as follows. On the basis of the acquired knowledge from the research of the

previous attempts in the field, an attempt was made to choose the appropriate neural network

structure for the purposes of forecasting a low liquid financial market such as the Bulgarian

one. Taking this particular feature of the domestic capital market into account, an appropriate

selection of input parameters was made for the selected forecasting model so that it could make

accurate predictions. The preliminary preparation and processing of the data was successfully

carried out, resulting in significant improvements to the outputs produced by the models. The

results clearly demonstrate the effectiveness of performing value transformations in changes

and averaging of input data. This manages to reduce the validation error significantly. There is

also a dependence of the magnitude of the calculated error of all the models used on the so-

called market situation. It has been found that for large amplitudes in the value of the stock

indices considered, known as the term volatility, the tendency of which is to increase in periods

when the market is in a trend and especially a lot in a downward trend when stock prices go

through a long period of decrease, artificial neural networks lose accuracy in their forecasts.

This is especially pronounced in a downward trend. There has been a tendency for neural

networks to perform well when forecasting on the basis of time series of financial information

for consolidation phase markets. Experiments for forecasting BSE-Sofia indices were

conducted with 3 types of neural networks and the results obtained are found to be good and

extremely interesting. A curious tendency has been found, namely, that the most commonly

used type of neural network, according to the scientific works described by the author, is that

the multilayer perceptron does not perform as successfully as the other two varieties - the neural

network with radial basis function and the most the precisely predicted neural network with

general regression. They seem to be much better at modeling input data, managing to produce

equally good results by isolating a different number of input parameters. For example, one of

the best performing general regression networks uses two neurons in the input layer

corresponding to the target variable, the latest value of the forecast index of the day and the

lowest value of the day, while another very successful model of a radial basis network uses all

4 input parameters provided to it. The author finds the attempt to call into question the validity

of the "Effective Market Hypothesis" to be successful, with the low levels of model error

making it suggest that new and more in-depth research in the field is likely to further improve

the results.

30

CHAPTER VI: PUBLICATIONS ON THE SUBJECT OF THESIS AND CIATATIONS

Shahpazov V., Doukovska L., Karastoyanov D., Artificial Intelligence Neural Networks

Applications in Forecasting Financial Markets and Stock Prices. Proc. of the International

Symposium on Business Modeling and Software Design – BMSD’14 Luxemburg, Grand

Duchy of Luxemburg, SCITEPRESS – Science and Technology Publications, 2014, ISBN:

978-989-758-032-1, DOI:10.5220/0005427202820288, 282 – 288.

Shahpazov V., Doukovska, Forecasting financial markets with artificial intelligence.

Proc. of the International Workshop on Advanced Control and Optimisation: Step Ahead

ACOSA’14 Bankya, Bulgaria, Prof. Marin Drinov Publishing House, 2014, ISSN:1314-4634.

67-74.

Shahpazov V., Velev V., Doukovska L., Forecasting Price Movement of Sofix Index on

the Bulgarian Stock Exchange – Sofia Using an Artificial Neural Network Model. Proc. of the

International Symposium on Business Modeling and Software Design – BMSD’13,

Noordwijkerhout, The Netherlands, SCITEPRESS – Science and Technology Publications,

2013, ISBN:978-989-8565-56-3, DOI:10.5220/0005427202820288, 298-303.

Shahpazov V., Velev V., Doukovska L., “Design and Application of Artificial Neural

Networks for Predicting the Values of Indexes on the Bulgarian Stock Market. Proc of the

Signal Processing Symposium – SPS’13, Jachranka Village, Poland, IEEEXplore, 2013,

ISBN:978-1-4673-6319-8-13, CD Proc.

Шахпазов В., Високочестотната търговия. Списание Техносфера ISSN 1313-3861

Брой 4 (34)/2016 г.

Shahpazov V.L., Popchev I., A Neural Network and Rule-based Systems Hybrid Model

for Forecasting the Capital Market, Международна Научна Конференция „Изкуствен

Интелект и Е-Лидерство “, Пловдив, Октомври 2019 г. (под печат)

Citations:

1. Samit Bahnja, Abhishek Das, Impact of Data Normalization on Deep Neural Network

for Time Series Forecasting, 2018

2. Cavalcante R.C., Brasiliero, R.C., Souza V.L., Nobrega J.P., Oliveira A.L.,

Computational Intelligence and Financial Markets: A Survey and Future Directions.

Expert Systems with Applications, 55, pp. 194-211, 2016.

3. Gabriel F.C. Campos, Rodrigo A. Igawa, Jos’e L. Seixas Jr., Alex M.G. de Almeida,

Rodrigo Capobianco Guidoy, Sylvio Barbon Jr., Supervised Approach for Indication

of Contrast Enhancement in Application of Image Segmentation, Proc. Of the Eighth

International Conference on Advances in Multimedia, ISBN 978-1-61208-452-7, pp.

12-18, 2016.

4. Tarun Dash, Vinayak Jaiswal, Anoosha Sagar, Gaurav Vazirani, Nupur Giri, Analysis

of associativity among mirror neurons for financial profiling, Proc. Of the Second

31

International Conference on Cognitive Computing and Information (CCIP), DOI

10.1109/CCIP.2016.7802869, 2016.

5. Tarun Dash, Vinayak Jaiswal, Anoosha Sagar, Gaurav Vazirani, Nupur Giri, Analysis

of associativity among mirror neurons for financial profiling: A proposal, Proc. of the

International Conference on Computing Communication Control and automation

(ICCUBEA), DOI 10.1109/ ICCUBEA.2016.780034, 2016.

6. Tukur U.M., S.M. Shamsuddin, Radial Basis Function Neural Network Learning with

Modified Backpropagation Algorithm. Indonesian Journal of Electrical Engeneering

and Computer Science, vol. 13, 2, pp. 369-378, 2015

All citations refer to the following:

Shahpazov V., V. Velev, L. Doukovska - Design and Application of Artificial Neural Networks

for Predicting the Values of Indexes on the Bulgarian Stock Market, Proc. of the Signal

Processing Symposium – SPS’13, Jachranka Village, Poland, CD, ISBN 978-1-4673-6319-8-

13- 2013 IEEE, 2013.

32

CHAPTER VII: SCIENTIFIC PROJECTS PARTICIPATIONS

- IICT Project - Intelligent Functional Diagnosis of Complex Systems and Investigation

of Uncertainty and Risk Structures (2011-2014).

- EEMPAM Project - “Building and Development of Young Highly Qualified Researchers for

Effective Application of Biomedical Research to Improve Quality of Life”, BG051PO001-

3.3.06-0048 / 04.10.2012

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